Details

sample321.0ms

Algorithm: halfpoints

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	2574
7	1165
6	432
5	178
4	111
3	79
2	48
1	30
0	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize92.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.2b	(- (exp x) (exp (- x)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 99

Calls

4 calls:

17.0ms	(+ (exp x) (exp (- x)))
45.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
51.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
21.0ms	(- (exp x) (exp (- x)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (exp x) (exp (- x)))
80.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
123.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
54.0ms	(- (exp x) (exp (- x)))

simplify1.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1758
1	517
0	199

prune865.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize149.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5)))
0.1b	(* 1/60 (pow x 5))
0.1b	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
0.2b	(* (* x x) 1/3)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`add-exp-log`
17×	`associate-l`
16×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
13×	`associate-r`
11×	`pow1`
10×	`times-frac`
8×	`prod-exp`
6×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative`
2×	`associate-+l+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `flip-+` `div-inv`

Counts

4 → 89

Calls

4 calls:

12.0ms	(+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5)))
9.0ms	(* 1/60 (pow x 5))
61.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
26.0ms	(* (* x x) 1/3)

series322.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5)))
73.0ms	(* 1/60 (pow x 5))
101.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
47.0ms	(* (* x x) 1/3)

simplify1.7s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
2	1534
1	474
0	184

prune924.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize144.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

38.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
84.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
37.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
11.0ms	(/ 1 (sqrt 2.0))

series629.0ms

Counts

4 → 10

Calls

4 calls:

212.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
273.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
144.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify2.3s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	2260
1	709
0	255

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize145.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

1128×	`sqrt-prod`
1116×	`times-frac`
592×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
79×	`add-exp-log`
49×	`add-cbrt-cube`
37×	`associate-/l*`
32×	`div-exp`
25×	`prod-exp`
24×	`associate-/r*`
23×	`pow1` `div-inv`
20×	`sqrt-pow1`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/` `associate-/l/`
2×	`inv-pow`
1×	`frac-times` `flip3-+` `associate-r` `associate-r/` `-commutative` `flip-+`

Counts

4 → 767

Calls

4 calls:

187.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
44.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
15.0ms	(/ 1 (sqrt (sqrt 2.0)))
52.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series465.0ms

Counts

4 → 8

Calls

4 calls:

302.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
163.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify2.4s

Counts

775 → 775

Iterations

Iter	Nodes
done	5000
1	1760
0	615

prune5.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes241.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end1.0ms

sample12.2s

Algorithm: halfpoints